HyperbolaHardBloom L3
Question
A conic pass through the point $(2,4)$ and is such that the segment of any of its tangents at any point contained between the co-ordinate is bisected at the point of tangency. Then the foci of the conic are:
Options
A.$(2\sqrt{2},0)$ and $( - 2\sqrt{2},0)$
B.$(2\sqrt{2},2\sqrt{2})$ and $( - 2\sqrt{2}, - 2\sqrt{2})$
C.$(4,4)$ and $( - 4, - 4)$
D.$(4\sqrt{2},4\sqrt{2})$ and $( - 4\sqrt{2}, - 4\sqrt{2})$
Solution
Sol. (c) $\left( \frac{dy}{dx} \right)_{(h,k)} = - \frac{k}{h}$
$$\begin{matrix} \Rightarrow & \frac{dy}{dx} = - \frac{y}{x} \\ \Rightarrow & ln(xy) = c \\ \Rightarrow & Put(2,4);c = ln8 \\ \Rightarrow & xy = 8 \\ & F_{1};F_{2} \equiv (4,4),( - 4, - 4) \end{matrix}$$
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